The present application relates to a method for estimating one or more parameters of a signal in an ultra wideband system, and a receiver for receiving ultra wideband signals. In particular, the methods and receivers according to one or more preferred embodiments may have particular application in delay and amplitude estimation in pulse based ultra wideband (UWB) systems, such as positioning systems.
In positioning systems, a pulse based ultra wideband (UWB) signal may be used to estimate the distance of the transmitter from the receiver by estimating signal arrival time at the receiver. Such a signal may also be used to estimate the direction of arrival (DOA) of a signal at the receiver, by comparing the signal amplitudes received by two directional antennae which have been placed in a fixed geometrical relationship to one another. A conventional method for estimating the signal arrival time is by measuring the amplitude of the received signal and the time at which it exceeds a threshold value is taken as the signal arrival time. The maximum amplitude value of the received signal is taken to be the strength of the signal.
The above conventional method is satisfactory in a free space condition, that is one in which there are no reflections. However, in a system where there are multiple reflections in the signal path, the reflection signals will overlap with the direct path signal and this will affect the timing and the amplitude values determined by the above conventional method. The received signal will be the sum of the direct-path and multipath signals.
To increase the signal to noise ratio (SNR), the cross-correlation between the received signal and a local stored pulse template may be calculated. Based on the cross-correlation function, the signal arrival time and amplitude may be estimated. This is equivalent to a matched filter. Unfortunately, cross-correlation cannot solve the multipath problem described above.
In the publication by Jian Li, and Renbiao Wu entitled “An efficient algorithm for time delay estimation” and published in IEEE Transaction on Signal Processing. Vol. 46. No. 8, August 1998, for the multipath delay mixed signal, a frequency domain time delay estimation approach was presented. The approach was formulated as a nonlinear least squares (NLS) fitting problem and solved by the Weighted Fourier transform and RELAXation (hereinafter referred to as WRELAX) technique, where it was shown that the delay estimation for every multipath element of the mixed signal may approach Cramer-Rao bound (CRB) and hence is optimal.
The WRELAX technique was also disclosed in the publication by Renbiao Wu, Jian Li, Zheng-shi Liu, entitled “Super resolution time delay estimation via MODE_WRELAX.” Published in IEEE Transaction Aerospace and Electronic Systems, Vol. 35, No. 1, January 1999, to achieve super resolution time-delay estimation.
When the dimensions of the signals (that is the number of multipath copies of the transmitted signal) are known, the WRELAX technique described in the publication by Jian Li, and Renbiao Wu entitled “An efficient algorithm for time delay estimation” and published in IEEE Transaction on Signal Processing. Vol. 46. No. 8, August 1998 performs satisfactorily. However, it becomes very time consuming when the number of multipaths is large, due to the multi-level iterations of the WRELAX technique, which makes operation in real-time difficult and complex.
Thus there is a need for an apparatus and method for calculating the amplitude and time of arrival of a signal from a multipath signal.